Expected Value Public Administration and Policy PAD634 Judgment and Decision Making Behavior Expected Value Thomas R. Stewart, Ph.D. Center for Policy Research Rockefeller College of Public Affairs and Policy University at Albany State University of New York T.STEWART@ALBANY.EDU Copyright © Thomas R. Stewart

Expected value Expected Value = P(O1)V(O1) + P(O2)V(O2) + P(O3)V(O3) + P(Oi) is the probability of outcome i V(Oi) is the value of outcome i ExpectedValue.ppt

Expected value One of many possible decision making rules The basis for decision analysis ExpectedValue.ppt

Hypothetical concrete pouring example Suppose that Jill is a contractor who pours concrete for foundations. She does not want to pour if it will rain before the concrete sets. ExpectedValue.ppt

Example of quantitative model: Concrete (flat-work) contractor Decision Don’t pour Pour Event Idle crew (-700) Remove ruined concrete and redo job (-5500) Rain Idle crew (-700) Successful pour (2000) No rain ExpectedValue.ppt

Decision tree for concrete pouring example: No forecast -5500 Rain .26 E.V. = Expected Value = .26  (-5500) + .74  (2000) = 50 E.V. = 50 2000 No rain .74 Pour -700 Don't pour With only climate information, decision is always to pour: Expected value = 50 ExpectedValue.ppt

Expected value Expected Value = P(O1)V(O1) + P(O2)V(O2) + P(O3)V(O3) + P(Oi) is the probability of outcome i V(Oi) is the value of outcome i ExpectedValue.ppt

Descriptive model of Jill's decision making process Jill looks at the sky in the morning and does not pour if it is cloudy. Rule 1: If cloudy, do not pour. Rule 2: If not cloudy, pour. ExpectedValue.ppt

Characteristics of cloudiness as predictor of rain ExpectedValue.ppt

Decision tree for concrete pouring example: Simple forecast Value of information = 140 - 50 = 90 -5500 2000 Rain No rain .20 .80 E.V. = 500 E.V. = 140 Pour (sky is clear) .70 Look at sky -700 Don't pour (clouds) .30 ExpectedValue.ppt

Probability of precipitation (POP) forecast Jill decides to use the forecast. She will not pour anytime the forecast indicates a 10% chance of rain or greater. ExpectedValue.ppt

Jill’s value of information 230 - 140 = 90 Decision tree for concrete pouring example: POP forecast with Jill’s decision rule Jill’s value of information 230 - 140 = 90 -5500 2000 Pour (POP < .10) Rain No rain .40 .05 .95 E.V. = 1625 E.V. = 230 Obtain POP forecast -700 Don't pour (POP  .10) .60 ExpectedValue.ppt

Prescriptive decision making process with forecast Expected value = 590 Pour if forecast is .20 or below ExpectedValue.ppt

Summary Climate information only E.V. = 50 Look at sky E.V. = 140 POP forecast, Jill’s cutoff E.V. = 230 POP forecast, optimal cutoff E.V. = 590 ExpectedValue.ppt